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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA system of particles has initial angular momentum \( \mathbf{L}(0) = (\hat{i} + 2\hat{j} + 5\hat{k})\text{ kg m}^2/\text{s} \). It is subjected to a time-varying net external torque \( \boldsymbol{\tau}_{\text{ext}}(t) = (4t\hat{i} + 2\hat{j})\text{ N m} \). The magnitude of the total angular momentum of the system at \( t = 2\text{ s} \) is:
Correct answer · Option 3
\( \sqrt{142}\text{ kg m}^2/\text{s} \)
Explanation
\( \mathbf{L}(2) = \mathbf{L}(0) + \int_0^2 (4t\hat{i} + 2\hat{j}) dt = (\hat{i} + 2\hat{j} + 5\hat{k}) + (8\hat{i} + 4\hat{j}) = 9\hat{i} + 6\hat{j} + 5\hat{k} \). Magnitude \( = \sqrt{9^2 + 6^2 + 5^2} = \sqrt{142}\text{ kg m}^2/\text{s} \).
